Trade Theory with Numbers: Quantifying the Welfare Consequences of Globalization

Trade Theory with Numbers: Quantifying the Welfare Consequences of Globalization Andrés Rodríguez-Clare (UC Berkeley and NBER) September 29, 2012

The Armington Model

The Armington Model CES preferences: This implies that U j = ( ) σ/(σ 1) Q (σ 1)/σ ij, σ > 1 i X ij = P1 σ ij k P 1 σ kj }{{} λ ij Y j }{{} total income

The Armington Model If wages are w i and (iceberg) trade costs are τ ij, then P ij = w i τ ij, so X ij = (w i τ ij ) 1 σ k (w k τ kj ) 1 σ Y j This is the Gravity Equation for the Armington model. We refer to σ 1 as the trade elasticity. Technically, d ln X ij /X jj d ln τ ij = σ 1

Armington: Trade and Welfare The expenditure function with CES preferences is e(p 1, P 2,..., P N, U) = ( i P 1 σ i ) 1/(1 σ) } {{ } P = "price index" U Expenditure per capita in country j is Y j /L j = w j, hence w j = P j U j and so U j = w j /P j. We can think of this as "real income in country j" We want to know how changes in trade costs affect w j /P j

Armington: Trade and Welfare Come back to Let Since P ij = w i τ ij and P 1 σ j λ ij = X ij = λ ij P1 σ ij k P 1 σ kj Y j X ij k X kj = X ij Y j = k P 1 σ kj P1 σ ij k P 1 σ kj then = (w i τ ij ) 1 σ P 1 σ j

Armington: Trade and Welfare So we have Since τ jj = 1, then λ ij = (w i τ ij ) 1 σ P 1 σ j λ jj = w j 1 σ Pj 1 σ = ( ) 1 σ wj P j Finally, U j = w j = λ 1/(1 σ) jj P j

Armington: Gains from Trade How bad would it be to shut down trade? In autarky have λ jj = 1, hence U A j /U j = λ 1/(σ 1) jj Define gains from trade as GT j 1 U A j /U j = 1 λ 1/(σ 1) jj Note that ε σ 1 is the trade elasticity, so can write GT j = 1 λ 1/ε jj

Armington: Gains from Trade To implement GT j = 1 λ 1/ε jj, need to measure λ jj and need an estimate of ε

Armington: Gains from Trade To implement GT j = 1 λ 1/ε jj, need to measure λ jj and need an estimate of ε λ jj is share of gross expenditure devoted to home purchases, computed from OECD-STAN as gross production - exports gross expenditure To estimate ε, return to gravity equation, X ij = (w i τ ij ) ε Pj ε Y j Taking logs, we have ln X ij = ε ln w i + ln ( Y j Pj ε ) ε ln τij If we had data for τ ij, then can run OLS regression of ln X ij on ln τ ij with exporter and importer dummies to estimate ε

Armington: Gains from Trade We have ln X ij = ε ln w i + ln ( Y j Pj ε ) ε ln τij + ξ ij

Armington: Gains from Trade We have How do we measure τ ij? ln X ij = ε ln w i + ln ( Y j Pj ε ) ε ln τij + ξ ij

Armington: Gains from Trade We have How do we measure τ ij? Tariffs ln X ij = ε ln w i + ln ( Y j Pj ε ) ε ln τij + ξ ij

Armington: Gains from Trade We have How do we measure τ ij? Tariffs Price differences ln X ij = ε ln w i + ln ( Y j Pj ε ) ε ln τij + ξ ij

Armington: Gains from Trade We have How do we measure τ ij? Tariffs Price differences A central estimate of ε is 5 ln X ij = ε ln w i + ln ( Y j Pj ε ) ε ln τij + ξ ij

Armington: Gains from Trade λ jj % GT j Canada 0.87 2.7 Denmark 0.89 2.2 France 0.91 1.8 Portugal 0.84 3.3 Slovakia 0.79 4.6 U.S. 0.95 1.0

Armington: Counterfactuals More generally, us implies that (notation ˆx = x /x) U j = w j = λ 1/ε jj P j Û j = λ 1/ε jj

Armington: Counterfactuals More generally, us implies that (notation ˆx = x /x) U j = w j = λ 1/ε jj P j Û j = λ 1/ε jj For ex-ante analysis, need to predict ˆλ jj

Armington: Counterfactuals More generally, us implies that (notation ˆx = x /x) U j = w j = λ 1/ε jj P j Û j = λ 1/ε jj For ex-ante analysis, need to predict ˆλ jj Two approaches

Armington: Counterfactuals More generally, us implies that (notation ˆx = x /x) U j = w j = λ 1/ε jj P j Û j = λ 1/ε jj For ex-ante analysis, need to predict ˆλ jj Two approaches Diffi cult: calibrate model and simulate counterfactual

Cheese, really?

Cheese, really? What about comparative advantage? (Ricardo, Eaton-Kortum)

Cheese, really? What about comparative advantage? (Ricardo, Eaton-Kortum) Variety gains? (Krugman)

Cheese, really? What about comparative advantage? (Ricardo, Eaton-Kortum) Variety gains? (Krugman) Selection/reallocation effects? (Melitz)

Cheese, really? What about comparative advantage? (Ricardo, Eaton-Kortum) Variety gains? (Krugman) Selection/reallocation effects? (Melitz) Pro-competitive effects? (Melitz-Ottaviano)

Comparative Advantage (Ricardo, Eaton-Kortum) Another reason to trade beyond cheese: specialization according to comparative advantage

Comparative Advantage (Ricardo, Eaton-Kortum) Another reason to trade beyond cheese: specialization according to comparative advantage In Ricardian theory, comparative advantage arises because of differences in technology

Comparative Advantage (Ricardo, Eaton-Kortum) Trade elasticity now comes from productivity rather than preferences (ε = θ rather than ε = σ 1)

Comparative Advantage (Ricardo, Eaton-Kortum) Trade elasticity now comes from productivity rather than preferences (ε = θ rather than ε = σ 1) But welfare implications of an international shock are still Ŵ j = λ 1/ε jj Given same data {λ ij, Y j }, same ε, and same shock { ˆτ ij }, then same ˆλ jj and same Ŵ j

Increasing Returns with Differentiated Goods (Krugman) In principle, gains from increasing returns and more variety

Increasing Returns with Differentiated Goods (Krugman) In principle, gains from increasing returns and more variety In practice, with CES preferences, both variety and scale unchanged

Increasing Returns with Differentiated Goods (Krugman) In principle, gains from increasing returns and more variety In practice, with CES preferences, both variety and scale unchanged Gains arise from cheaper foreign goods, just as in Armington

Reallocation Effects (Melitz) Fixed exporting costs > only highly productive firms export

Reallocation Effects (Melitz) Fixed exporting costs > only highly productive firms export Trade > reallocation of labor from low to high productivity firms

Reallocation Effects (Melitz) Fixed exporting costs > only highly productive firms export Trade > reallocation of labor from low to high productivity firms Trade > higher average effi ciency

Reallocation Effects (Melitz) Fixed exporting costs > only highly productive firms export Trade > reallocation of labor from low to high productivity firms Trade > higher average effi ciency But what about welfare? First problem: in Melitz, heterogeneity in productivity, but same VMPL across firms Second problem: exit of low productivity firms entails a loss of variety

Pro-competitive Effects? Key idea: stronger competition weakens domestic monopolies, improving effi ciency

Pro-competitive Effects? Key idea: stronger competition weakens domestic monopolies, improving effi ciency But: lower tariffs allow foreign monopolists to increase their markups

Pro-competitive Effects? Key idea: stronger competition weakens domestic monopolies, improving effi ciency But: lower tariffs allow foreign monopolists to increase their markups Which effect dominates? It depends on the model Edmon-Midrigan-Xu drop MC and use Cournot competition Calibrate to Taiwanese firm-level data There can be large pro-competitive effects of trade through destruction of monopolies

Pro-competitive Effects? Two ways to go: drop MC or drop CES

Pro-competitive Effects? Two ways to go: drop MC or drop CES Edmon-Midrigan-Xu drop MC and use Cournot competition

Pro-competitive Effects? Two ways to go: drop MC or drop CES Edmon-Midrigan-Xu drop MC and use Cournot competition Calibrate to Taiwanese firm-level data

Pro-competitive Effects? Two ways to go: drop MC or drop CES Edmon-Midrigan-Xu drop MC and use Cournot competition Calibrate to Taiwanese firm-level data There can be large pro-competitive effects of trade through destruction of monopolies Formally, trade reduces dispersion in markups

Pro-competitive Effects? Two ways to go: drop MC or drop CES

Pro-competitive Effects? Two ways to go: drop MC or drop CES Edmon-Midrigan-Xu drop MC and use Cournot competition

Pro-competitive Effects? Two ways to go: drop MC or drop CES Edmon-Midrigan-Xu drop MC and use Cournot competition Arkolakis, Costinot, Donaldson and RC drop CES but keep Pareto (to get gravity)

Pro-competitive Effects? Two ways to go: drop MC or drop CES Edmon-Midrigan-Xu drop MC and use Cournot competition Arkolakis, Costinot, Donaldson and RC drop CES but keep Pareto (to get gravity) Markup distribution not affected: incumbents lower markups, but low markup firms leave Non-homothetic preferences imply that a decline in trade costs reallocates demand towards low markup goods

Back to Armington 1. Add multiple sectors 2. Add traded intermediates

Multiple sectors, GT Upper level EoS ρ and lower level EoS ε s Recall gains for Canada of 2.7%. Now gains can be much higher: ρ = 1 implies GT = 8%

Multiple sectors, GT, role of upper level EoS

Tradable intermediates, GT Set ρ = 1, add tradable intermediates with Input-Output structure Labor shares are 1 α j,s and input shares are α j,ks ( k α j,ks = α j,s )

Tradable intermediates, GT % GT j % GT MS j % GT IO j Canada 2.7 8.0 19.2 Denmark 2.2 6.1 15.3 France 1.8 3.5 10.5 Portugal 3.3 9.1 26 U.S. 1.0 1.8 4.4

Combination of micro and macro features In Krugman, free entry leads to scale effects associated with total sales

Combination of micro and macro features In Krugman, free entry leads to scale effects associated with total sales In Melitz, additional scale effects associated with market size

Combination of micro and macro features In Krugman, free entry leads to scale effects associated with total sales In Melitz, additional scale effects associated with market size In both models, trade may affect entry and fixed costs All these effects do not play a role in the one sector model

Gains from Trade... Canada China Germany New Zealand US Aggregate 2.7 0.8 2 2.5 1

Gains from Trade... Canada China Germany New Zealand US Aggregate 2.7 0.8 2 2.5 1 MS, PC 8 1.1 3.7 6.9 1.8

Gains from Trade... Canada China Germany New Zealand US Aggregate 2.7 0.8 2 2.5 1 MS, PC 8 1.1 3.7 6.9 1.8 Key: Cobb-Douglas preferences

Gains from Trade... Canada China Germany New Zealand US Aggregate 2.7 0.8 2 2.5 1 MS, PC 8 1.1 3.7 6.9 1.8 MS, MC 8.9-0.2 4.6 2.1 1.3

Gains from Trade... Canada China Germany New Zealand US Aggregate 2.7 0.8 2 2.5 1 MS, PC 8 1.1 3.7 6.9 1.8 MS, MC 8.9-0.2 4.6 2.1 1.3 Key: scale effects linked to entry and L.O.V., compositional effect

Gains from Trade... Canada China Germany New Zealand US Aggregate 2.7 0.8 2 2.5 1 MS, PC 8 1.1 3.7 6.9 1.8 MS, MC 8.9-0.2 4.6 2.1 1.3 MS, IO, PC 19.2 5.9 9.8 14.3 4.4

Gains from Trade... Canada China Germany New Zealand US Aggregate 2.7 0.8 2 2.5 1 MS, PC 8 1.1 3.7 6.9 1.8 MS, MC 8.9-0.2 4.6 2.1 1.3 MS, IO, PC 19.2 5.9 9.8 14.3 4.4 Key: IO loops and interdependencies

Gains from Trade... Canada China Germany New Zealand US Aggregate 2.7 0.8 2 2.5 1 MS, PC 8 1.1 3.7 6.9 1.8 MS, MC 8.9-0.2 4.6 2.1 1.3 MS, IO, PC 19.2 5.9 9.8 14.3 4.4 MS, IO(k), PC 26.8 9.3 14.3 19.8 6.7 Key: further amplification through trade in capital goods

Gains from Trade... Canada China Germany New Zealand US Aggregate 2.7 0.8 2 2.5 1 MS, PC 8 1.1 3.7 6.9 1.8 MS, MC 8.9-0.2 4.6 2.1 1.3 MS, IO, PC 19.2 5.9 9.8 14.3 4.4 MS, IO(k), PC 26.8 9.3 14.3 19.8 6.7 MS, IO, MC, η s = 0 25.1 23.2 16.8 10.3 5.8 Key: trade expands markets relative to entry cost > entry

Gains from Trade... Canada China Germany New Zealand US Aggregate 2.7 0.8 2 2.5 1 MS, PC 8 1.1 3.7 6.9 1.8 MS, MC 8.9-0.2 4.6 2.1 1.3 MS, IO, PC 19.2 5.9 9.8 14.3 4.4 MS, IO(k), PC 26.8 9.3 14.3 19.8 6.7 MS, IO, MC, η s = 0 25.1 23.2 16.8 10.3 5.8 MS, IO, MC, η s = 1.5 33.6 44.8 25.5 14.9 10.1

From GT to trade policy evaluation Back to {λ ij, Y j }, ε and { ˆτ ij } to get implied ˆλ jj

From GT to trade policy evaluation Back to {λ ij, Y j }, ε and { ˆτ ij } to get implied ˆλ jj This is what CGE exercises do

From GT to trade policy evaluation Back to {λ ij, Y j }, ε and { ˆτ ij } to get implied ˆλ jj This is what CGE exercises do Contribution here:

From GT to trade policy evaluation Back to {λ ij, Y j }, ε and { ˆτ ij } to get implied ˆλ jj This is what CGE exercises do Contribution here: Link to theory "mid-sized models"

From GT to trade policy evaluation Back to {λ ij, Y j }, ε and { ˆτ ij } to get implied ˆλ jj This is what CGE exercises do Contribution here: Link to theory "mid-sized models" Model consistent estimation

Fit of model Research agenda

Research agenda Fit of model Elasticities

Research agenda Fit of model Elasticities Scale Effects

Final Thoughts Complementarities between trade and MP/diffusion can increase GT

Final Thoughts Complementarities between trade and MP/diffusion can increase GT Gains from openness (including MP, diffusion) can be much larger

Final Thoughts Complementarities between trade and MP/diffusion can increase GT Gains from openness (including MP, diffusion) can be much larger How can small countries be rich?

Final Thoughts Complementarities between trade and MP/diffusion can increase GT Gains from openness (including MP, diffusion) can be much larger How can small countries be rich? Gains from openness + domestic frictions Scale economies = y DNK /y US = 1/3